But the Rams made their supporters sweat over their first home victory of the season against opponents who played for more than an hour with 10 men following the dismissal of the defender Richard Dunne.
Paradoxically, Derby were more impressive while the numbers remained even, but although the sending-off did not change the course of the game it incensed the Everton manager, Walter Smith, who said: "The referee had a major bearing on the game. His first-half performance was nothing short of diabolical." Smith added that Dunne did not make contact with Stefan Schnoor before the booking - one of nine in an even-tempered match - which prompted his dismissal in the 25th minute.
Derby were already well on top and should have taken the lead after only two minutes when Rory Delap found Fuertes with a beautifully weighted ball down the left and sprinted 40 yards to get his head to the resulting cross. The Everton goalkeeper, Paul Gerrard, was stranded, but Richard Gough had positioned himself perfectly to head the ball off the line.
Everton had little opportunity to add to the eight goals they had scored in the previous seven days. The Derby defender Spencer Prior saw his header from Lars Bohinen's free-kick flash over the bar, and Seth Johnson's dribbling down the left earned a series of free-kicks on the edge of the box which might have paid greater dividends had not Horacio Carbonari tried to demolish rather than evade the Everton wall.
Derby squandered another chance to take the lead shortly after Dunne's dismissal when Fuertes broke down the middle and unselfishly chose to lay the ball off to the better-placed Schnoor, who hoisted it over the crossbar from 10 yards with only Gerrard to beat.
The break saw the introduction of the Italian duo Francesco Baiano and Stefano Eranio for Derby, but it was less the combination of fresh legs and the extra man than Everton's loss of concentration which produced the goal two minutes later.
From a short corner Baiano floated a cross to the far post, where Fuertes was able to head home unchallenged.
It forced Everton, who had pulled everyone but Kevin Campbell back behind the ball since Dunne's departure, to show more adventure, and as so often happens, the 10 men discovered that attack is the best form of defence. Carbonari had to halt Campbell with a flying lunge that earned him a booking, and when Derby did make their numerical superiority tell they tended towards over- elaborate approach work and speculative efforts from long range or tight angles. Darryl Powell, Derby's most impressive player, sent a 25-yard drive narrowly over the bar and Delap chipped the ball on to the roof of the net when a cross to a colleague would have been wiser.
Such was the threat posed by Everton's late surge that Delap, who started the match as a striker, was withdrawn to his more familiar position of wingback as Derby clung on. But even then Everton were unlucky not to equalise when Don Hutchison's dipping effort finished on the roof of the net.